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Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof
This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.
Psychology and Mathematics Education
Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "erro...
Advances in Mathematics Education Research on Proof and Proving
This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.
International Reflections on the Netherlands Didactics of Mathematics
This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education.
Is God a Moral Monster?
A recent string of popular-level books written by the New Atheists have leveled the accusation that the God of the Old Testament is nothing but a bully, a murderer, and a cosmic child abuser. This viewpoint is even making inroads into the church. How are Christians to respond to such accusations? And how are we to reconcile the seemingly disconnected natures of God portrayed in the two testaments? In this timely and readable book, apologist Paul Copan takes on some of the most vexing accusations of our time, including: God is arrogant and jealous God punishes people too harshly God is guilty of ethnic cleansing God oppresses women God endorses slavery Christianity causes violence and more Copan not only answers God's critics, he also shows how to read both the Old and New Testaments faithfully, seeing an unchanging, righteous, and loving God in both.
Cultural Apologetics
Renewing the Christian voice, conscience, and imagination so that we can become compelling witnesses of the Gospel in today's culture. Christianity has an image problem. While the culture we inhabit presents us with an increasingly anti-Christian and disenchanted position, the church in the West has not helped its case by becoming anti-intellectual, fragmented, and out of touch with the relevancy of Jesus to all aspects of contemporary life. The muting of the Christian voice, its imagination, and its collective conscience have diminished the prospect of having a genuine missionary encounter with others today. Cultural apologetics attempts to demonstrate not only the truth of the Gospel but a...
God and the New Physics
An explanation of how recent discoveries of the new physics are revolutionizing our view of the world and, in particular, throwing light on many of the questions formerly posed by religion
Passionate Conviction
Popular Christian apologists, from Emir Caner to N.T. Wright, present their dynamic defenses of faith in Passionate Conviction.
